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September 18, 2025AppliedMath2 citationsOpen Access

Mathematical Modeling of Heat Transfer and Energy Efficiency in Above-Ground Outdoor Pools

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ŁDŁukasz DziubińskiPCPaweł ChwietczukSLSeweryn Lipiński

Key Points

  • Optimizing pool geometry can significantly enhance the energy efficiency of above-ground pools, reducing operational costs.
  • The analysis showed that daytime circulation boosts solar heat gains, while nighttime losses increase due to convection and radiation.
  • Transparent covers effectively reduce evaporation but may limit solar input, affecting overall heating efficiency.
  • Heating in colder climates is highly energy-intensive due to low ambient temperatures and wind conditions, emphasizing the need for cost-effective solutions.

Abstract

Above-ground outdoor swimming pools are increasingly popular due to their affordability and ease of installation, yet maintaining optimal water temperature under variable climate conditions remains challenging. Our study develops a theoretical and mathematical modeling framework to quantify heat gains and losses in residential frame pools, focusing on convection, radiation, and evaporation as dominant mechanisms. The analysis demonstrates that daytime water circulation enhances solar heat gains but increases nighttime losses, while opaque covers reduce evaporation at the expense of solar input. Heating during colder months in Central and Eastern Europe is highly energy-intensive due to low ambient temperatures, strong winds, and reduced solar radiation. Based on these findings, the paper proposes cost-effective strategies, including optimized pool geometry, wind protection, transparent covers, and operational adjustments such as daytime-only circulation. The model provides a foundation for advanced simulations and supports the design of sustainable heating solutions, aiming to extend the swimming season and reduce operational costs.

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Cite This Study

Dziubiński et al. (2025) studied this question.

synapsesocial.com/papers/68d461d231b076d99fa61744https://doi.org/10.3390/appliedmath5030124
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